Controlling chaos in a Lorenz-like system using feedback

We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or even steady state. The range of control depends critically on the feedback delay time and amplitude. Our experimental results are compared with the complex Lorenz equations which show good agreement.

Controlling the complex Lorenz equations by modulation

We demonstrate that a system obeying the complex Lorenz equations in the deep chaotic regime can be controlled to periodic behavior by applying a modulation to the pump parameter. For arbitrary modulation frequency and amplitude there is no obvious simplification of the dynamics. However, we find that there are numerous windows where the chaotic system has been controlled to different periodic behaviors. The widths of these windows in parameter space are narrow, and the positions are related to the ratio of the modulation frequency of the pump to the average pulsation frequency of the output variable. These results are in good agreement with observations previously made in a far-infrared laser system.

Experimental control of single-mode laser chaos by using continuous, time-delayed feedback

Control of chaos in the single-mode optically pumped far-infrared (NH3)-N-15 laser is experimentally demonstrated using continuous time-delay control. Both the Lorenz spiral chaos and the detuned period-doubling chaos exhibited by the laser have been controlled. While the laser is in the Lorenz spiral chaos regime the chaos has been controlled both such that the laser output is cw, with corrections of only a fraction of a percent necessary to keep it there, and to period one. The laser has also been controlled while in the period-doubling chaos regime, to both the period-one and -two states.

Observation of generalized synchronization of chaos in a driven chaotic system

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the driving signal.

Factors controlling the origin of gas in Australian Bowen Basin coals

Open system pyrolysis (heating rate 10 degrees C/min) of coal maturity (vitrinite reflectance, VR) sequence (0.5%, 0.8% and 1.4% VR) demonstrates that there are two stages of thermogenic methane generation from Bowen Basin coals. The first and major stage shows a steady increase in methane generation maximising at 570 degrees C, corresponding to a VR of 2-2.5%. This is followed by a less intense methane generation which has not as yet maximised by 800 degrees C (equivalent to VR of 5%). Heavier (C2+) hydrocarbons are generated up to 570 degrees C after which only the C-1 (CH4, CO and CO2) gases are produced. The main phase of heavy hydrocarbon generation occurs between 420 and 510 degrees C. Over this temperature range,methane generation accounts for only a minor component, whereas the wet gases (C-2-C-5) are either in equal abundance or are more abundant by a factor of two than the liquid hydrocarbons. The yields of non-hydrocarbon gases CO2 and CO are greater then methane during the early stages of gas generation from an immature coal, subordinate to methane during the main phase of methane generation after which they are again dominant. Compositional data for desorbed and produced coal seam gases from the Bowen show that CO2 and wet gases are a minor component. This discrepancy between the proportion of wet gas components produced during open system pyrolysis and that observed in naturally matured coals may be the result of preferential migration of wet gas components, by dilution of methane generated during secondary cracking of bitumen, or kinetic effects associated with different activations for production of individual hydrocarbon gases. Extrapolation of results of artificial pyrolysis of the main organic components in coal to geological significant heating rates suggests that isotopically light methane to delta(13)C of -50 parts per thousand can be generated. Carbon isotope depletions in C-13 are further enhanced, however, as a result of trapping of gases over selected rank levels (instantaneous generation) which is a probable explanation for the range of delta(13)C values we have recorded in methane desorbed from Bowen Basin coals (-51 +/- 9 parts per thousand). Pervasive carbonate-rich veins in Bowen Basin coals are the product of magmatism-related hydrothermal activity. Furthermore, the pyrolysis results suggest an additional organic carbon source front CO2 released at any stage during the maturation history could mix in varying proportions with CO2 from the other sources. This interpretation is supported by C and O isotopic ratios, of carbonates that indicate mixing between magmatic and meteoric fluids. Also, the steep slope of the C and O isotope correlation trend suggests that the carbonates were deposited over a very narrow temperature interval basin-wide, or at relatively high temperatures (i.e., greater than 150 degrees C) where mineral-fluid oxygen isotope fractionations are small. These temperatures are high enough for catagenic production of methane and higher hydrocarbons from the coal and coal-derived bitumen. The results suggests that a combination of thermogenic generation of methane and thermodynamic processes associated with CH4/CO2 equilibria are the two most important factors that control the primary isotope and molecular composition of coal seam gases in the Bowen Basin. Biological process are regionally subordinate but may be locally significant. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Controlling leucine zipper specificity with interfacial hydrophobic residues

Dimerisation of leucine zippers results from the parallel association of alpha-helices to form a coiled coil. Coiled coils comprise a heptad repeat, denoted as (abcdefg)(n), where residues at positions a and d are hydrophobic and constitute the core of the dimer interface. Charged amino acids at the e and g positions of the coiled coil are thought to be the major influence on dimerisation specificity through the formation of attractive and repulsive interhelical electrostatic interactions. However, the variability of a-position residues in leucine zipper transcription factors prompted us to investigate their influence on dimerisation specificity. We demonstrate that mutation of a single interfacial a-position Ala residue to either Val, Ile or Leu significantly alters the homo- and heterodimerisation specificities of the leucine zipper domain from the c-Jun transcription factor. These results illustrate the importance of a-position residues in controlling leucine zipper dimerisation specificity in addition to providing substantial contributions to dimer stability.

Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits: diffusive growth in the energy, or heating,'' while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.

Atoms in an amplitude-modulated standing wave - dynamics and pathways to quantum chaos

Cold rubidium atoms are subjected to an amplitude-modulated far-detuned standing wave of light to form a quantum-driven pendulum. Here we discuss the dynamics of these atoms. Phase space resonances and chaotic transients of the system exhibit dynamics which can be useful in many atom optics applications as they can be utilized as means for phase space state preparation. We explain the occurrence of distinct peaks in the atomic momentum distribution, analyse them in detail and give evidence for the importance of the system for quantum chaos and decoherence studies.

Quantum chaos in atom optics

I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonians are time dependent. Thus we shall consider systems with a potential function that has a higher than quadratic dependence on the position and, furthermore, we shall allow the potential function to be a periodic function of time. This is the simplest class of Hamiltonian system that can exhibit chaotic dynamics. I shall show how such systems can be realized in atom optics, where very cord atoms interact with optical dipole potentials of a far-off resonance laser. Such systems are ideal for quantum chaos studies as (i) the energy of the atom is small and action scales are of the order of Planck's constant, (ii) the systems are almost perfectly isolated from the decohering effects of the environment and (iii) optical methods enable exquisite time dependent control of the mechanical potentials seen by the atoms.

Quantum chaos in the atomic gravitational cavity

We report quantum chaos phenomena in the atomic gravitational cavity. We consider the reflection of cold atoms from a temporally modulated evanescent wave. In the globally chaotic regime, for small modulation, the squared energy distribution as a function of time demonstrates dynamical localization. However, for larger modulation delocalization occurs.

Controlling the decoherence of a ''meter'' via stroboscopic feedback

We propose a simple modification of the experimental scheme employed by Brune rt ni. [Phys. Rev. Lett. 79, 4887 (1996)] for the generation and detection of a Schrodinger cat state, in which the decoherence of the cat state can be significantly slowed down using an appropriate feedback.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Metastable chaos in the ammonia ring laser

We report experimental studies of metastable chaos in the far-infrared ammonia ring: laser. When the laser pump power is switched from above chaos threshold to slightly below, chaotic intensity pulsations continue for a varying time afterward before decaying to either periodic or cw emission. The behavior is in good qualitative agreement with that predicted by the Lorenz equations, previously used to describe this laser. The statistical distribution of the duration of the chaotic transient is measured and shown to be in excellent agreement with the Lorenz equations in showing a modified exponential distribution. We also give a brief numerical analysis and graphical visualization of the Lorenz equations in phase space illustrating the boundary between the metastable chaotic and the stable fixed point basins of attraction. This provides an intuitive understanding of the metastable dynamics of the Lorenz equations and the experimental system.